To graph the line with a slope of $-2$ passing through the point $(-4, -1)$, follow these steps:

1. Plot the Point: Start by locating the point $(-4, -1)$ on the graph. Go 4 units to the left on the $x$-axis and 1 unit down on the $y$-axis to find this point. Mark it clearly.

2. Use the Slope: The slope $m = -2$ means that for every 1 unit you move to the right along the $x$-axis, you move 2 units down along the $y$-axis (because of the negative sign).

3. Find Another Point: Starting from $(-4, -1)$, move 1 unit to the right (to $-3$ on the $x$-axis) and 2 units down. This will take you to the point $(-3, -3)$. Plot this second point.

4. Draw the Line: Use a ruler or the line tool provided in the graphing interface to draw a straight line through both points. Extend this line across the grid to represent the entire line.

5. Check Alignment: Ensure that the line has the correct slope by verifying that every movement of 1 unit right corresponds to a drop of 2 units down along the line.

Would you like more detailed steps, or do you have any specific questions?

Here are five related questions for deeper understanding:

1. How would the line look if the slope were positive instead of negative?
2. What changes if the line passes through a different point but has the same slope?
3. How can you write the equation of this line in slope-intercept form?
4. How would you graph a line with an undefined slope through a given point?
5. What effect does changing the slope value have on the steepness of the line?

Tip: Remember, the slope indicates the steepness and direction of the line: positive slopes go up to the right, while negative slopes go down to the right.